Re: problem of arithmetic modulo
- From: Dave Seaman <dseaman@xxxxxxxxxxxx>
- Date: Wed, 23 Jan 2008 12:27:57 +0000 (UTC)
On Tue, 22 Jan 2008 21:19:25 -0800, William Elliot wrote:
On Tue, 22 Jan 2008, Bill wrote:
We have 3^1000 = sum(a_i 10^i) where a_i are the digits of 3^1000Let dj = a_j.
expressed in decimal system.
let 's say c=sum(a_i) the sum over all digits.
the value of c modulo 3 equals 0 and it's easily solved.
But what 's about c modulo 7 ?
3^1000 = sum_j dj.10^j = 3 * sum_j dj (mod 7)
3^6 = 1 (mod 7)
3^1000 = (3^6)^166 * 3^4 = 3 * 3^3 = 3 * 27 = -3 (mod 7)
sum_j dj = -1 = 6 (mod 7)
Mathematica 6.0 for Mac OS X x86 (64-bit)
Copyright 1988-2007 Wolfram Research, Inc.
In[1]:= Mod[Plus @@ IntegerDigits[3^1000], 7]
Out[1]= 0
--
Dave Seaman
Oral Arguments in Mumia Abu-Jamal Case heard May 17
U.S. Court of Appeals, Third Circuit
<http://www.abu-jamal-news.com/>
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